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mathematics
statistics

Fundamentals Of Statistics 4th Edition Michael Sullivan III - Solutions

In many parliamentary procedures, a supermajority is deﬁned as an excess of 60% of voting members. In a poll conducted by the Gallup organization on May 10, 1939, 1561 adult Americans were asked, “Do you think the United States will have to ﬁght Japan within your lifetime?” Of the 1561
A Zone diet is one with a 40%–30%–30% distribution of carbohydrate, protein, and fat, respectively, and is based on the book Enter the Zone. In a study conducted by researchers Christopher Gardner and associates, 79 subjects were administered the Zone diet. After 12 months, the mean weight loss
According to the Pew Research Center, the proportion of the American population who use only a cellular telephone (no land line) is 0.37. Jason conducts a survey of thirty 20- to 24-year-olds who live on their own and ﬁnds that 16 do not have a land line to their home. Does this provide
According to the U.S. Census Bureau, 10.5% of registered births in the United States in 2007 were to teenage mothers. A sociologist believes that this percentage has increased since then. (a) Determine the null and alternative hypotheses, (b) Explain what it would mean to make a Type I error, and
According to the Center on Philanthropy at Indiana University, the mean charitable contribution per household among households with income of $1 million or more in the United States in 2005 was $17,072. A researcher believes that the level of giving has changed since then. (a) Determine the null
According to the National Association of Home Builders, the mean price of an existing single-family home in 2009 was $218,600. A real estate broker believes that because of the recent credit crunch, the mean price has decreased since then. (a) Determine the null and alternative hypotheses, (b)
Federal law requires that a jar of peanut butter that is labeled as containing 32 ounces must contain at least 32 ounces. A consumer advocate feels that a certain peanut butter manufacturer is shorting customers by underﬁlling the jars. (a) Determine the null and alternative hypotheses, (b)
The standard deviation in the pressure required to open a certain valve is known to be σ = 0.7 psi. Due to changes in the manufacturing process, the quality-control manager feels that the pressure variability has been reduced. (a) Determine the null and alternative hypotheses, (b) Explain what
According to the Centers for Disease Control and Prevention, 19.6% of children aged 6 to 11 years are overweight. A school nurse thinks that the percentage of 6- to 11-year-olds who are overweight is higher in her school district. (a) Determine the null and alternative hypotheses, (b) Explain
According to the CTIA–The Wireless Association, the mean monthly cell phone bill was $47.47 in 2010. A researcher suspects that the mean monthly cell phone bill is different today. (a) Determine the null and alternative hypotheses, (b) Explain what it would mean to make a Type I error, and (c)
In 2010, the standard deviation SAT score on the Critical Reading Test for all students taking the exam was 112. A teacher believes that, due to changes to high school curricula, the standard deviation of SAT math scores has decreased. (a) Determine the null and alternative hypotheses, (b) Explain
According to popcorn.org, the mean consumption of popcorn annually by Americans is 54 quarts. The marketing division of popcorn.org unleashes an aggressive campaign designed to get Americans to consume even more popcorn. (a) Determine the null and alternative hypotheses that would be used to test
The mean score on the SAT Math Reasoning exam is 516. A test preparation company states that the mean score of students who take its course is higher than 516. (a) Determine the null and alternative hypotheses. (b) If sample data indicate that the null hypothesis should not be rejected, state the
According to the Centers for Disease Control and Prevention, in 2008, 6.7% of 12- to 17-year-olds had used marijuana in the previous 6 months. The Drug Abuse and Resistance Education (DARE) program underwent several major changes to keep up with technology and issues facing students in the 21st
According to the Centers for Disease Control, 15.2% of American adults experience migraine headaches. Stress is a major contributor to the frequency and intensity of headaches. A massage therapist feels that she has a technique that can reduce the frequency and intensity of migraine headaches. (a)
The following is an excerpt from a Consumer Reports article. The platinum Gasaver makes some impressive claims. The device, $188 for two, is guaranteed to increase gas mileage by 22% says the manufacturer, National Fuelsaver. Also, the company quotes “the government” as concluding,
The manufacturer of Prolong Engine Treatment claims that if you add one 12-ounce bottle of its $20 product your engine will be protected from excessive wear. An infomercial claims that a woman drove 4 hours without oil, thanks to Prolong. Consumer Reports magazine tested engines in which they added
Refer to Problem 18. Researchers must choose the level of signiﬁcance based on the consequences of making a Type I error. In your opinion, is a Type I error or Type II error more serious? Why? On the basis of your answer, decide on a level of signiﬁcance, Be sure to support your opinion.
If the consequences of making a Type I error are severe, would you choose the level of signiﬁcance, α, to equal 0.01, 0.05, or 0.10? Why?
What happens to the probability of making a Type II error, β, as the level of signiﬁcance, α, decreases? Why?
In your own words, explain the difference between “beyond all reasonable doubt” and “beyond all doubt.” Use these phrases to explain why we never “accept” the statement in the null hypothesis.
Determine the critical value for a right-tailed test regarding a population proportion at the α = 0.01 level of signiﬁcance.
Determine the critical value for a two-tailed test regarding a population proportion at the α = 0.05 level of signiﬁcance.
H0: p = 0.3 versus H1: p > 0.3n = 200; x = 75; α = 0.05Test the hypothesis using(a) The classical approach and(b) The P-value approach.Be sure to verify the requirements of the test.
H0: p = 0.6 versus H1: p < 0.6 n = 250; x = 124; α = 0.01 Test the hypothesis using (a) The classical approach and (b) The P-value approach. Be sure to verify the requirements of the test.
H0: p = 0.55 versus H1: p < 0.55 n = 150; x = 78; α = 0.1 Test the hypothesis using (a) The classical approach and (b) The P-value approach. Be sure to verify the requirements of the test.
H0: p = 0.25 versus H1: p < 0.25 n = 400; x = 96; α = 0.1 Test the hypothesis using (a) The classical approach and (b) The P-value approach. Be sure to verify the requirements of the test.
H0: p = 0.9 versus H1: p ≠ 0.9 n = 500; x = 440; α = 0.05 Test the hypothesis using (a) The classical approach and (b) The P-value approach. Be sure to verify the requirements of the test.
H0: p = 0.4 versus H1: p ≠ 0.4 n = 1000; x = 420; α = 0.01 Test the hypothesis using (a) The classical approach and (b) The P-value approach. Be sure to verify the requirements of the test.
Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 100 companies to invest in. After 1 year, 53 of the companies were considered winners;
Suppose an acquaintance claims to have the ability to determine the birth month of randomly selected individuals. To test such a claim, you randomly select 80 individuals and ask the acquaintance to state the birth month of the individual. If the individual has the ability to determine birth month,
Lipitor is meant to reduce total cholesterol and LDL cholesterol. In clinical trials, 19 out of 863 patients taking 10 mg of Lipitor daily complained of ﬂulike symptoms. Suppose that it is known that 1.9% of patients taking competing drugs complain of ﬂulike symptoms. Is there evidence to
Nexium is a drug that can be used to reduce the acid produced by the body and heal damage to the esophagus due to acid reﬂux. The manufacturer of Nexium claims that more than 94% of patients taking Nexium are healed within 8 weeks. In clinical trials, 213 of 224 patients suffering from acid
In April 2009, the Gallup organization surveyed 676 adults aged 18 and older and found that 352 believed they would not have enough money to live comfortably in retirement. Does the sample evidence suggest that a majority of adults in the United States believe they will not have enough money in
There are two major college entrance exams that a majority of colleges accept for admission, the SAT and ACT. ACT looked at historical records and established 21 as the minimum score on the ACT reading portion of the exam for a student to be considered prepared for social science in college.An
In August 2003, 56% of employed adults in the United States reported that basic mathematical skills were critical or very important to their job. The supervisor of the job placement ofﬁce at a 4-year college thinks this percentage has increased due to increased use of technology in the
In December 2001, 38% of adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. In a recent poll, 403 of 1122 adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. Has the proportion of families
In 1994, 52% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 256 of 800 parents of children in high school felt it was a serious problem that high school students were not being
In 2000, 58% of females aged 15 years of age and older lived alone, according to the U.S. Census Bureau. A sociologist tests whether this percentage is different today by conducting a random sample of 500 females aged 15 years of age and older and ﬁnds that 285 are living alone. Is there
In August 2002, 47% of parents who had children in grades K–12 were satisﬁed with the quality of education the students receive. In September 2010, the Gallup organization conducted a poll of 1013 parents who have children in grades K–12 and asked if they were satisﬁed with the quality of
According to menstuff.org, 22% of married men have “strayed” at least once during their married lives.(a) Describe how you might go about administering a survey to assess the accuracy of this statement.(b) A survey of 500 married men results in 122 indicating that they have “strayed” at
In a survey conducted by the American Animal Hospital Association, 37% of respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian found this result hard to believe, so he randomly selected 150 pet owners and discovered that 54 of them spoke to their pet
According to a survey conducted by the Association for Dressings and Sauces (this is an actual association!), 85% of American adults eat salad at least once a week. A nutritionist suspects that the percentage is higher than this. She conducts a survey of 200 American adults and ﬁnds that 171 of
Professors Honey Kirk and Diane Lerma of Palo Alto College developed a “learning community curriculum that blended the developmental mathematics and the reading curriculum with a structured emphasis on study skills.” In a typical developmental mathematics course at Palo Alto College, 50% of the
In 1997, 4% of mothers smoked more than 21 cigarettes during their pregnancy. An obstetrician believes that the percentage of mothers who smoke 21 cigarettes or more is less than 4% today. She randomly selects 120 pregnant mothers and ﬁnds that 3 of them smoked 21 or more cigarettes during
According to the U.S. Census Bureau, in 2009, 2.1% of Americans worked at home. An economist believes that the percentage of Americans working at home has increased since then. He randomly selects 150 working Americans and ﬁnds that 6 of them work at home. Do a higher proportion of Americans work
According to the U.S. Census Bureau, in 2009, 7.8% of Americans had a travel time to work of more than 60 minutes. An urban economist believes that the percentage of Americans who have a travel time to work of more than 60 minutes has increased since then. She randomly selects 80 working Americans
One of the more popular statistics reported in the media is the president’s job approval rating. The approval rating is reported as the proportion of Americans who approve of the job that the sitting president is doing and is typically based on a random sample of registered voters.(a) This
In November 2009, 65% (0.65) of Americans favored the death penalty for a person convicted of murder. In November 2010, 1025 adult Americans were asked by the Gallup organization, “Are you in favor of the death penalty for a person convicted of murder?” Of the 1025 adults surveyed, 653
According to Gallup, 21% of Americans consider themselves to be liberal. The Sullivan Statistics Survey asked respondents to disclose their political philosophy: Conservative, Liberal, Moderate. Treat the results of the Sullivan Statistics Survey as a random sample of adult Americans. Do the survey
According to the Centers for Disease Control, in 2008, 21% of adult Americans age 18 or older were current smokers. Treat the results of the Sullivan Statistics Survey as a random sample of adult Americans. Do the survey results suggest that the proportion of adult Americans who are current smokers
For every NFL game there is a team that is expected to win by a certain number of points. In betting parlance, this is called the spread. For example, if the Chicago Bears are expected to beat the Green Bay Packers by 3 points, a sports bettor would say, €œChicago is minus three.€ So, if the
In the United States, historically, 40% of registered voters are Republican. Suppose you obtain a simple random sample of 320 registered voters and ﬁnd 142 registered Republicans.(a) Consider the hypotheses H0: p = 0.4 versus H1: p < 0.4. Explain what the researcher would be testing. Perform
Suppose you wish to ﬁnd out the answer to the age-old question, “Do Americans prefer Coke or Pepsi?” You conduct a blind taste test in which individuals are randomly asked to drink one of the colas ﬁrst, followed by the other cola,and then asked to disclose which drink they prefer. Results
Simulate drawing 100 simple random samples of size n = 40 from a population whose proportion is 0.3.(a) Test the null hypothesis H0: p = 0.3 versus H1: p ≠ 0.3 for each simulated sample.(b) If we test the hypothesis at the α = 0.1 level of signiﬁcance, how many of the 100 samples would you
Simulate drawing 100 simple random samples of size n = 15 from a population whose proportion is 0.2. (a) Test the null hypothesis H0: p = 0.2 versus H1: p ≠ 0.2 for each simulated sample. (b) If we test the hypothesis at the α = 0.1 level of signiﬁcance, how many of the 100 samples would you
Based on historical birthing records, the proportion of males born worldwide is 0.51. In other words, the commonly held belief that boys are just as likely as girls is false. Systematic lupus erythematosus (SLE), or lupus for short, is a disease in which one’s immune system attacks healthy cells
Yale University graduate student J. Kiley Hamlin conducted an experiment in which 16 ten-month-old babies were asked to watch a climber character attempt to ascend a hill. On two occasions, the baby witnesses the character fail to make the climb. On the third attempt, the baby witnesses either a
Explain what a P-value is. What is the criterion for rejecting the null hypothesis using the P-value approach?
Suppose we are testing the hypothesis H0: p = 0.3 versus H1: p > 0.3 and we ﬁnd the P-value to be 0.23. Explain what this means. Would you reject the null hypothesis? Why?
Suppose we are testing the hypothesis H0: p = 0.65 versus H1: p ≠ 0.65 and we ﬁnd the P-value to be 0.02. Explain what this means. Would you reject the null hypothesis? Why?
Discuss the advantages and disadvantages of using the Classical Approach to hypothesis testing. Discuss the advantages and disadvantages of using the P-value approach to hypothesis testing.
(a) Determine the critical value for a right-tailed test of a population mean at the α = 0.01 level of signiﬁcance with 15 degrees of freedom. (b) Determine the critical value for a left-tailed test of a population mean at the α = 0.05 level of signiﬁcance based on a sample size of n =
(a) Determine the critical value for a right-tailed test of a population mean at the α = 0.1 level of signiﬁcance with 22 degrees of freedom. (b) Determine the critical value for a left-tailed test of a population mean at the α = 0.01 level of signiﬁcance based on a sample size of n = 40. (c)
To test H0: µ = 50 versus H1: µ < 50, a simple random sample of size n = 24 is obtained from a population that is known to be normally distributed.(a) If x̄ = 47.1 and s = 10.3, compute the test statistic.(b) If the researcher decides to test this hypothesis at the α = 0.05 level of
To test H0: µ = 40 versus H1: µ 7 40, a simple random sample of size n = 25 is obtained from a population that is known to be normally distributed.(a) If x̄ = 42.3 and s = 4.3, compute the test statistic.(b) If the researcher decides to test this hypothesis at the α = 0.1 level of
To test H0: µ = 100 versus H1: µ ≠ 100, a simple random sample of size n = 23 is obtained from a population that is known to be normally distributed.(a) If x̄ = 104.8 and s = 9.2, compute the test statistic.(b) If the researcher decides to test this hypothesis at the α = 0.01 level of
To test H0: µ = 80 versus H1: µ < 80, a simple random sample of size n = 22 is obtained from a population that is known to be normally distributed.(a) If x̄ = 76.9 and s = 8.5, compute the test statistic.(b) If the researcher decides to test this hypothesis at the α = 0.02 level of
To test H0: µ = 20 versus H1: < 6 20, a simple random sample of size n = 18 is obtained from a population that is known to be normally distributed.(a) If x̄ = 18.3 and s = 4.3, compute the test statistic.(b) Draw a t-distribution with the area that represents the P-value shaded.(c) Approximate
To test H0: µ = 4.5 versus H1: µ > 4.5, a simple random sample of size n = 13 is obtained from a population that is known to be normally distributed.(a) If x̄ = 4.9 and s = 1.3, compute the test statistic.(b) Draw a t-distribution with the area that represents the P-value shaded.(c)
To test H0: µ = 105 versus H1: µ ≠ 105, a simple random sample of size n = 35 is obtained.(a) Does the population have to be normally distributed to test this hypothesis by using the methods presented in this section? Why?(b) If x̄ = 101.9 and s = 5.9, compute the test statistic.(c) Draw a
To test H0: µ = 45 versus H1: µ ≠ 45, a simple random sample of size n = 40 is obtained.(a) Does the population have to be normally distributed to test this hypothesis by using the methods presented in this section? Why?(b) If x̄ = 48.3 and s = 8.5, compute the test statistic.(c) Draw a
According to the Crown ATM Network, the mean ATM withdrawal is $67. PayEase, Inc., manufacturers an ATM that allows one to pay bills (electric, water, parking tickets, and so on), as well as withdraw money. A review of 40 withdrawals shows the mean withdrawal is $73 from a PayEase ATM machine. Do
In 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from the Centers for Disease Control and Prevention’s Advance Data Report, No. 347. Suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 63.9
The ACT is a college entrance exam. In addition to administering this exam, researchers at ACT gauge high school students’ readiness for college-level subjects. For example, ACT has determined that a score of 22 on the mathematics portion of the ACT suggests that a student is ready for
Do students who learned English as well as another language simultaneously score worse on the SAT Critical Reading exam than the general population of test takers? The mean score among all test takers on the SAT Critical Reading exam is 501. A random sample of 100 test takers who learned English as
In a study published in the American Journal of Psychiatry (157:737–744, May 2000), researchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents. The hippocampus is the portion of the brain responsible for long-term memory storage. The
Resin Para-nonylphenol is found in polyvinyl chloride (PVC) used in the food processing and packaging industries. Researchers wanted to determine the effect this substance had on the organ weight of ﬁrst-generation mice when both parents were exposed to 50 micrograms per liter (µg>L) of
A Fair Isaac Corporation (FICO) score is used by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. Its value ranges from 300 to 850. An individual with a FICO score over 700 is considered to be a quality credit risk. According to Fair Isaac
According to the American Time Use Survey, the typical American spends 154.8 minutes (2.58 hours) per day watching television. Do Internet users spend less time each day watching television? A survey of 50 Internet users results in a mean time watching television per day of 128.7 minutes, with a
In 2002, the mean age of an inmate on death row was 40.7 years, according to data obtained from the U.S. Department of Justice. A sociologist wondered whether the mean age of a death-row inmate has changed since then. She randomly selects 32 death-row inmates and ﬁnds that their mean age is 38.9,
In 2001, the mean household expenditure for energy was $1493, according to data obtained from the U.S. Energy Information Administration. An economist wanted to know whether this amount has changed signiﬁcantly from its 2001 level. In a random sample of 35 households, he found the mean
The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 84.3 seconds. A manager devises a new drive-through system that he believes will decrease wait time. He initiates the new system at his restaurant and measures
Michael Sullivan, son of the author, decided to enroll in a reading course that allegedly increases reading speed and comprehension. Prior to enrolling in the class, Michael read 198 words per minute (wpm). The following data represent the words per minute read for 10 different passages read after
Calcium is essential to tree growth because it promotes the formation of wood and maintains cell walls. In 1990, the concentration of calcium in precipitation in Chautauqua, New York, was 0.11 milligram per liter (mg/L). A random sample of 10 precipitation dates in 2010 results in the following
A certain brand of apple juice is supposed to have 64 ounces of juice. Because the penalty for underï¬lling bottles is severe, the target mean amount of juice is 64.05 ounces. However, the ï¬lling machine is not precise, and the exact amount of juice varies from bottle to bottle. The
In 2007, Apple stock had a mean daily volume of 35.1 million shares, according to Yahoo!Finance. A random sample of 40 trading days in 2010 resulted in a sample mean of 23.6 million shares with a standard deviation of 11.7 million shares.(a) Based on the histogram and boxplot shown (from
Google became a publicly traded company in August 2004. Initially, the stock traded over 10 million shares each day! Since the initial offering, the volume of stock traded daily has decreased substantially. In 2007, the mean daily volume in Google stock was 5.44 million shares, according to
Test the hypotheses in Problem 23 by constructing a 99% conï¬dence interval.
Test the hypotheses in Problem 24 by constructing a 95% conï¬dence interval.
Test the hypotheses in Problem 25 by constructing a 95% conﬁdence interval.
Test the hypotheses in Problem 26 by constructing a 95% conﬁdence interval.
A math teacher claims that she has developed a review course that increases the scores of students on the math portion of the SAT exam. Based on data from the College Board, SAT scores are normally distributed with µ = 515. The teacher obtains a random sample of 1800 students, puts them through
The manufacturer of a daily dietary supplement claims that its product will help people lose weight. The company obtains a random sample of 950 adult males aged 20 to 74 who take the supplement and ﬁnds their mean weight loss after 8 weeks to be 0.9 pound with standard deviation weight loss of
According to the credit reporting agency Transunion, the mean credit card debt in the United States among individuals with credit cards for the period between April and June of 2010 was $4951. Treating the results of the StatCrunch survey as a random sample of U.S. residents, determine whether
According to the Nielsen’s Television Audience Report, the mean number of televisions per household in 2009 was 2.9. Treating the results of the StatCrunch survey as a random sample of U.S. residents, determine whether there is evidence to suggest the number of televisions per household has risen
The mean IQ score of humans is 100. Suppose the director of Institutional Research at Joliet Junior College (JJC) obtains a simple random sample of 40 JJC students and ﬁnds the mean IQ is 103.4 with a standard deviation of 13.2.(a) Consider the hypotheses H0: µ = 100 versus H1: µ > 100.
Simulate drawing 100 simple random samples of size n = 15 from a population that is normally distributed with mean 100 and standard deviation 15.(a) Test the null hypothesis H0: µ = 100 versus H1: µ ≠ 100 for each of the 100 simple random samples.(b) If we test this hypothesis at the α = 0.05
The exponential probability distribution can be used to model waiting time in line or the lifetime of electronic components. Its density function is skewed right. Suppose the wait-time in a line can be modeled by the exponential distribution with µ = σ = 5 minutes.(a) Simulate obtaining 100
An abstract in a journal article is a short synopsis of the study. The following abstract is from an article in the British Medical Journal (BMJ). The article uses relative risk in the analysis, which is common in health-related studies. Relative risk represents how many times more likely an

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